1. Field of the Invention
This invention relates to methods and systems for transforming data arrays defining input data values from source locations to target locations defined by a multidimensional coordinate system. The invention relates to methods and systems for spatially transforming images particularly in respect to data samples corresponding to picture elements of images for display on visual display devices such as cathode ray tubes. The invention further relates to methods and systems for providing spatial transformations in a multidimensional coordinate system using separate transformations for each coordinate direction of the system and more particularly to a method and system providing spatial transformations of a two-dimensional video image in a raster scan television system.
2. Discussion of the Prior Art
Methods of producing multidimensional spatial transformations have been developed and are discussed in references such as Principles of Interactive Computer Graphics by William M. Newman and Robert F. Sproull, McGraw-Hill Book Company, second edition 1979, Transmission And Display of Pictorial Information, by D. E. Pearson, A Halstead Press Book, 1975 and "A Digital Signal Processing Approach to Interpolation", by Ronald W. Schaefer and Lawrence R. Rabiner, Proc. IEEE, Vol. 61, pp. 692-702, June 1973. However, for transformations which involve rotation, perspective representations, or other transformations which involve more than simple unidirectional translations, or scaling, the transformation process involved simultaneous multidimensional spatial filtering and interpolation operations. Consequently, a video image transformation process required complex and time consuming processing for each picture element of the transformed video image. Transformations have been thus rendered impractical in terms of cost of data processing time for complex images such as raster scan television displays. The long processing times required further made the real time processing of a continuous stream of television frames virtually impossible with present day technology.
Nevertheless, a practical system for transforming multidimensional visual images has an important demand for such diverse purposes as producing special effects in television programming or transforming a satellite picture of the earth which is distorted by the curvature of the earth into a flat pictorial representation.